Section  consists largely of background material on the perverse Leray filtration on cohomology. After setting up notation, we prove that this filtration is respected by two localization exact sequences (Proposition REF ). We then briefly review some results of de Cataldo and Migliorini [1]} (Theorem REF ), which give a geometric interpretation of the perverse Leray filtration, before using these to prove a series of useful vanishing lemmas for the graded pieces. We conclude the section with a result from [2]} (Proposition REF ), which shows that the perverse Leray filtration on the cohomology of \(Y\)  coincides with the one induced by cup-product with the preimage of a general linear section.
